Hypothesis: Asking whether Muslims and Christians believe in the same God is the same as asking whether geocentrism and heliocentrism are descriptions of the same universe.
So do they describe the same universe or not?
The question is not best seen as followed by an instruction to check the yes or no box. If you’re asking whether contrary theories to explain the same fact are about the same fact, then the answer is (analytically) yes. If you’re asking whether contrary theories to explain the same fact are the same (i.e. not contrary) then the answer is (again, analytically) no. Rather, the question becomes interesting when we ask what relation contrary accounts have to the thing they are accounting for.
When St. Thomas raises the same question in ST 1.13.10 his answer is that no one uses a word to signify X except to signify the real X, and that even when we are mistaken in our significations this does not change our orientation to speaking of a thing as it is. Since all our accounts arise from an orientation to the truth, mistaken accounts are dependent on this basic orientation, which gives contrary significations of one word an intrinsic order to one meaning (i.e. the true one). Contrary accounts of one word or fact (like “God”) are therefore instances of what STA calls an analogous name.
Just Thomism 